After roughly three days of deliberation, the jury awarded the $965 million to 14 family members and the FBI agent.

Connecticut Superior Court Judge Barbara Bellis had previously issued a default judgment against Mr. Jones after he failed to provide information about his business and other communications required during the court proceedings.

Mr. Jones for years claimed the shooting in Newtown, Conn., in which a gunman killed 20 first-graders and six adults, didn’t happen and the victims were actually “crisis actors.” The Connecticut case is one of several lawsuits seeking to hold him liable for his statements. Families who sued say they have been subject to repeated harassment from Mr. Jones’s followers who believed the families were part of a conspiracy.

The award follows a Texas jury’s decision in August that ordered Mr. Jones to pay about $50 million to the parents of a 6-year-old who was killed in the shooting. That trial took place in Austin, where Infowars and Mr. Jones are based. Another trial is expected there. A bankruptcy proceeding is under way, as well, involving Infowars parent company Free Speech Systems LLC, which could delay any payments the families receive.

“I know that this is not the end of Alex Jones. His hate, lies and conspiracy theories will follow both me and my family all of our days,” said Erica Lafferty, whose mother, Sandy Hook’s principal, died in the 2012 shooting. “I’m proud and thankful for the message that was sent today, that the truth matters. And those who profit off others’ trauma will pay for what they have done.”

Chris Mattei, the lawyer who represented the families and FBI agent, said he would work to enforce the verdict, and added that his firm will be active in the bankruptcy court proceedings. 

Neither Mr. Jones’s lawyer Norm Pattis nor an Infowars representative immediately responded to requests for comment.

Mr. Jones, who wasn’t in court for the verdict, ran a broadcast while it was being announced, deriding the jury’s award and asking for donations from his viewers. He said the money will go toward appeals and bankruptcy costs.

Family members of those who died took the stand during the Connecticut proceedings and tearfully told jurors about how Mr. Jones’s statements affected their lives. 

Some said they received death and rape threats and moved multiple times to avoid recognition.

Robbie Parker, whose daughter Emilie was killed, testified that a statement he gave to the media in the days after the shooting was aired on Infowars repeatedly, as Mr. Jones and other hosts on Infowars claimed he was an actor. 

Mr. Parker said Emilie’s memorial page was inundated with comments claiming they were liars and calling their daughter vulgar names. Over the years, he said the relentless coverage led to encounters online with people who believed he was a liar, and at least once, an in-person confrontation. 

Mr. Parker received the largest individual damages award from the jury: $120 million.  

Mr. Jones’s attorneys told jurors that he shouldn’t be responsible for sweeping damages, and argued that he shouldn’t be the scapegoat for what happened to the families. Mr. Jones offered running commentary about the trial on his show, as well as outside the courthouse, criticizing the judge and the proceedings. On the stand, he said he was done apologizing for the shooting and called the plaintiffs’ attorneys ambulance chasers.

Infowars has an online site, a streaming platform and a radio show. During trial, the families’ lawyers presented evidence from Infowars’ parent company that indicated its platform received hundreds of millions of page views. They argued that Mr. Jones’s audience grew in the wake of his Sandy Hook claims, making him millions of dollars.

Before the start of the Connecticut trial, Mr. Jones put Infowars parent company Free Speech Systems into chapter 11 bankruptcy in an effort to contain the costs of the defamation litigation. After the trial began, a Texas bankruptcy judge ordered an independent review of Infowars’ financial affairs and blocked FSS from hiring chapter 11 advisers chosen by Mr. Jones.

The Sept. 20 bench ruling represented a setback for Mr. Jones’s attempt to use the bankruptcy to limit Sandy Hook liability for Infowars. The review, which is being conducted by an independent trustee, will examine payments by FSS to Mr. Jones before the chapter 11 case and roughly $54 million in debt the company owes to an affiliate managed by Mr. Jones’ father.

—Jonathan Randles contributed to this article.

Write to Erin Mulvaney at erin.mulvaney@wsj.com